Mobile robots and autonomous guided vehicles have become an indispensable part of modern industrial environments and are used for a wide range of handling operations. To fully use the potential of mobile platforms, omnidirectional platforms are a good choice. A prominent and widely used variant in the industry are Mecanum wheels, which allow arbitrary movement in any direction in the plane. In most applications only the kinematics is considered, however, dynamic models that take the geometry of the rollers into account are still missing. In this paper two models for Mecanum wheels with different degrees of detail are derived. The detailed model considers the rollers as single bodies undergoing contact and friction with the rolling plane. As the wheel consists of multiple rollers, a complex contact situation with temporal overlapping and additional vibrations occurs. The simplified model reproduces the overall kinematics of the rollers with orthotropic friction and only one rigid body for the wheel, thereby being computationally more efficient. Both models are well suited to reproduce essential dynamic effects of a mobile robotic platform, which can not be described by the conventional kinematics model. We implement and compare both models with experimental results, showing the good performance of both models.